Question

Construct a triangle ABC in which BC is 5 cm, Angle B is ${60}^{\circ }$ and AB-AC=0 cm. What type of triangle is this?

• A. Equilateral
• B. Isosceles
• C. Scalene
• D. It is not possible to construct this triangle

Answer 1

The correct option is A Equilateral

Steps- -Draw line segment BC=5 cm. Draw ray BX which makes an angle ${60}^{\circ }$ with BC.

-Cut off line segment BD of length AB-AC on BX on the opposite side of BC. But AB-AC is 0. Hence point B and point D are the same.

-Draw the perpendicular bisector of BC. Let the perpendicular bisector intersect ray BX at A.

-Angle ABC is the required triangle.

By inspection it can be observed that the triangle obtained is an equilateral triangle.